Number Sense: Making math intuitive

© 2008 Gwen Dewar, Ph.D., all rights reserved

In his excellent book, opens in a new windowThe Number Sense: How the Mind Creates Mathematics, Revised and Updated Edition, Stanislas Dehaene argues that kids go astray when teachers emphasize calculation over conceptual understanding.

Left to their own devices, kids discover strategies that make math meaningful. Unfortunately, notwithstanding, kids are frequently taught that these strategies are incorrect.

At least, that's what happens in Western countries like the United states of america and France–countries where students spend a lot of time being drilled on the mechanics of adding. Kids are chastised for counting on their fingers considering this is somehow viewed as cheating. And so are kids who use shortcut strategies to solve problems.

For example, Dehaene says, a child might solve the problem

vi+vii=?

By recalling that 6+vi =12 and that 7 is i more than 6. Ergo, 6+7 = 13.

Or, Dehaene says, consider this instance from an experiment conducted by Jeffrey Bisanz.

Bisanz presented American 6 year olds and 9 year olds with this problem:

v + iii – iii = ?

The vi-twelvemonth olds tended to solve this without doing whatsoever calculations. They simply observed that the positive 3 and the negative 3 cancel each other out.

But the nine-year olds (who had learned from their teachers what the "right" approach was) were more probable to take the long route to the answer:

5 + 3 = viii

eight – iii = 5

In other words, 9 year olds had learned that they should follow the instructor's procedure kickoff, and call back afterwards.

This reminds me of my own babyhood, when I was learning multiplication. What is vii x 8? If I couldn't call up, I'd add together a string of 7 8s. Since I hated memorizing my timetables, I ended upwards doing a lot of sums.

Hardly a clever shortcut, and it was decumbent to mistake because I'd sometimes lose track. Only at least it helped me understand the meaning of multiplication. It fabricated things very concrete and intuitive.

According to Dehaene, ane of the most common errors that kids make when presented with elementary multiplication problem like

vii ten viii = ?

is to add together the two numbers together:

7 x eight = 15

So what's worse? Using the clumsy-but-meaningful strategy of adding upwards a string of 8s, only to miscount and come upwards with seven x viii = 48?

Or misunderstanding the whole point and adding together 7 and 8?

Dehaene favors pregnant. When kids are trained to emphasize procedures over meaning, they fail to develop an intuitive sense of number.

And that leads to all kinds of trouble…confusion, boredom, a poorly adult number sense, and (perhaps) a lifelong dislike of math.

Dehaene's tips for making math intuitive

Dehaene argues that we tin can foster our children's sense of quantity by grounding mathematics knowledge in concrete, familiar situations. For instance, when we teach our kids subtraction, nosotros can present kids with the concrete operation of removing apples from a basket.

And here are more than recommendations from Dehaene:

• Let kids count on their fingers
• Teach kids about fractions by having them envision the division of a pie
• Teach kids virtually negative numbers by having kids think of temperatures.

More than information

Humans aren't the only ones with a bit of number sense, and even human babies tin can perform certain mental calculations. For more data, see my evidence-based guide to the opens in a new windowdevelopment of number sense.

In addition to highlights of the latest research, it includes more than research-based for encouraging math skills in immature children.

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References: Number Sense

Dehaene S. 1997. The number sense: How the heed creates mathematics. New York: Oxford University Printing.

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Source: https://parentingscience.com/number-sense/